a(n) = total number of different ways a grasshopper can take n hops.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =7a(7) =12a(8) =21a(9) =37a(10) =63a(11) =116a(12) =208a(13) =372a(14) =682a(15) =1255a(16) =2334a(17) =4277a(18) =7951a(19) =14905a(20) =27967a(21) =52334a(22) =98222a(23) =186344a(24) =352621a(25) =666933a(26) =1264406a(27) =2413511a(28) =4604124a(29) =8766995